Find the length of the parametric curve described by
\[(x,y) = (2 \sin t, 2 \cos t)\]from $t = 0$ to $t = \pi.$
Explanation: The curve describes a semicircle with radius 2.  Therefore, the length of the curve is
\[\frac{1}{2} \cdot 2 \pi \cdot 2 = \boxed{2 \pi}.\][asy]
unitsize(1 cm);

pair moo (real t) {
  return (2*sin(t),2*cos(t));
}

real t;
path foo = moo(0);

for (t = 0; t <= pi; t = t + 0.01) {
  foo = foo--moo(t);
}

draw((-2.5,0)--(2.5,0));
draw((0,-2.5)--(0,2.5));
draw(foo,red);

label("$2$", (1,0), S);

dot("$t = 0$", moo(0), W);
dot("$t = \pi$", moo(pi), W);
[/asy]